Privacy Structure and Blackwell Frontier

TL;DR

This paper characterizes the set of feasible posterior distributions under graph-based privacy constraints, linking extreme points to semi-chains and providing algorithms for their construction, advancing understanding of privacy-utility trade-offs.

Contribution

It introduces a novel characterization of feasible posteriors using semi-chains and spanning trees, connecting privacy constraints with graph theory.

Findings

Characterization of feasible posterior distributions under privacy constraints

Connection established between extreme posteriors and semi-chains

Algorithms for constructing semi-chains via spanning trees

Abstract

This paper characterizes the set of feasible posterior distributions subject to graph-based inferential privacy constraint, including both differential and inferential privacy. This characterization can be done through enumerating all extreme points of the feasible posterior set. A connection between extreme posteriors and strongly connected semi-chains is then established. All these semi-chains can be constructed through successive unfolding operations on semi-chains with two partitions, which can be constructed through classical spanning tree algorithm. A sharper characterization of semi-chains with two partitions for differential privacy is provided.